Three identical particles are located at the vertices of an equilateral triangle. Each particle moves along a meridian with equal speed towards the centroid and collides inelastically. (a) all the three particles will bounce back along the meridians with lesser speed. (b) all the three particles will become stationary. (c) all the particles will continue to move in their original directions but with lesser speed (d) nothing can be said

Options

A. (a) all the three particles will bounce back along the meridians with lesser speed.
B. (b) all the three particles will become stationary.
C. (c) all the particles will continue to move in their original directions but with lesser speed
D. (d) nothing can be said

Answer

To solve the problem, we need to analyze the situation of the three identical particles moving towards the centroid of an equilateral triangle and their behavior after they collide inelastically.

### Step-by-Step Solution:

1. **Understanding the Initial Setup**:
- We have three identical particles located at the vertices of an equilateral triangle.
- Each particle moves towards the centroid of the triangle with equal speed.

2. **Analyzing the Motion Towards the Centroid**:
- The centroid of an equilateral triangle is the point where all three medians intersect, and it is located at an equal distance from all three vertices.
- Since all particles are moving towards the centroid, they will meet at this point.

3. **Collision Type**:
- The problem states that the collision is inelastic. In an inelastic collision, the particles stick together or move as a single entity after the collision.
- The total momentum of the system before the collision must be conserved.

4. **Momentum Conservation**:
- Before the collision, each particle has a momentum given by \( p = mv \), where \( m \) is the mass of each particle and \( v \) is their speed.
- The total momentum of the system before the collision is the vector sum of the momenta of the three particles.

5. **After the Collision**:
- After colliding inelastically, the particles will move together as a single entity.
- The speed of this combined entity can be determined using the conservation of momentum. Since they collide inelastically, they will not bounce back but rather move together with a new speed.

6. **Final State**:
- Since the particles are identical and collide inelastically, they will not bounce back along their original paths. Instead, they will move together with a speed that is less than the initial speed of the individual particles, but they will not stop completely.

### Conclusion:
Given the analysis, the correct answer is:
(c) all the particles will continue to move in their original directions but with lesser speed.